Non-minimality of corners in subriemannian geometry

We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.Comment: 11 pages, final versio

Effects of Marangoni numbers on thermocapillary drop migration: constant for quasi-steady state?

The overall {\it steady}-state energy balance with two phases in a flow domain requires that the change in energy of the domain is equal to the difference between the total energy entering the domain and that leaving the domain. From the condition, the integral thermal flux across the surface is studied for a {\it steady} thermocapillary drop migration in a flow field with uniform temperature gradient at small and large Marangoni (Reynolds) numbers. The drop is assumed to have only a slight axisymmetric deformation from a sphere. It is identified that a conservative/nonconservative integral thermal flux across the surface in the {\it steady} thermocapillary drop migration at small/large Marangoni (Reynolds) numbers. The conservative flux confirms the assumption of {\it quasi-steady} state in the thermocapillary drop migration at small Marangoni (Reynolds) numbers. The nonconservative flux may well result from the invalid assumption of {\it quasi-steady} state, which indicates that the thermocapillary drop migration at large Marangoni (Reynolds) numbers cannot reach {\it steady} state and is thus a {\it unsteady} process.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1112.276

Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings

We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered spectral projector, and some geometric hypothesis on the local behaviour of the eigenvalues at the crossings

Ochrobactrum sp. MPV1 from a dump of roasted pyrites can be exploited as bacterial catalyst for the biogenesis of selenium and tellurium nanoparticles

Background: Bacteria have developed different mechanisms for the transformation of metalloid oxyanions to non-toxic chemical forms. A number of bacterial isolates so far obtained in axenic culture has shown the ability to bioreduce selenite and tellurite to the elemental state in different conditions along with the formation of nanoparticles-both inside and outside the cells-characterized by a variety of morphological features. This reductive process can be considered of major importance for two reasons: firstly, toxic and soluble (i.e. bioavailable) compounds such as selenite and tellurite are converted to a less toxic chemical forms (i.e. zero valent state); secondly, chalcogen nanoparticles have attracted great interest due to their photoelectric and semiconducting properties. In addition, their exploitation as antimicrobial agents is currently becoming an area of intensive research in medical sciences. Results: In the present study, the bacterial strain Ochrobactrum sp. MPV1, isolated from a dump of roasted arsenopyrites as residues of a formerly sulfuric acid production near Scarlino (Tuscany, Italy) was analyzed for its capability of efficaciously bioreducing the chalcogen oxyanions selenite (SeO32-) and tellurite (TeO32-) to their respective elemental forms (Se0 and Te0) in aerobic conditions, with generation of Se- and Te-nanoparticles (Se- and TeNPs). The isolate could bioconvert 2 mM SeO32- and 0.5 mM TeO32- to the corresponding Se0 and Te0 in 48 and 120 h, respectively. The intracellular accumulation of nanomaterials was demonstrated through electron microscopy. Moreover, several analyses were performed to shed light on the mechanisms involved in SeO32- and TeO32- bioreduction to their elemental states. Results obtained suggested that these oxyanions are bioconverted through two different mechanisms in Ochrobactrum sp. MPV1. Glutathione (GSH) seemed to play a key role in SeO32- bioreduction, while TeO32- bioconversion could be ascribed to the catalytic activity of intracellular NADH-dependent oxidoreductases. The organic coating surrounding biogenic Se- and TeNPs was also characterized through Fourier-transform infrared spectroscopy. This analysis revealed interesting differences among the NPs produced by Ochrobactrum sp. MPV1 and suggested a possible different role of phospholipids and proteins in both biosynthesis and stabilization of such chalcogen-NPs. Conclusions: In conclusion, Ochrobactrum sp. MPV1 has demonstrated to be an ideal candidate for the bioconversion of toxic oxyanions such as selenite and tellurite to their respective elemental forms, producing intracellular Se- and TeNPs possibly exploitable in biomedical and industrial applications.[Figure not available: see fulltext.

Extremal curves in nilpotent Lie groups

We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It turns out that abnormal extremals are precisely the horizontal curves contained in algebraic varieties of a specific type. We also extend the results to the nonfree case.Comment: 30 pages, final versio

Linalool, a plant-derived monoterpene alcohol, reverses doxorubicin resistance in human breast adenocarcinoma cells

Essential oils from various aromatic plants have been reported to exert chemopreventive and/or antitumor effects. In addition, a number of studies have shown the ability of chemopreventive phytochemicals to increase the sensitivity of cancer cells to conventional anticancer drugs. The success of chemotherapeutic agents is often hindered by the development of drug resistance, with multidrug resistant (MDR) phenotypes reported in a number of tumors, generally involving reduced intracellular drug accumulation due to increased drug efflux by membrane transporters. In the present study, the effects of linalool (LIN), a monoterpene alcohol found in the essential oils from many aromatic plants, on the growth of two human breast adenocarcinoma cell lines, MCF7 WT and multidrug resistant MCF7 AdrR, were investigated, both as a single agent and in combination with doxorubicin (DOX). The results reported here show that LIN only moderately inhibits cell proliferation; interestingly, however, subtoxic concentrations of LIN potentiate DOX-induced cytotoxicity and pro-apoptotic effects in both cell lines. A significant synergism can be observed in MCF7 AdrR cells, which may be due, at least in part, to the ability of LIN to increase DOX accumulation and to induce a decrease in Bcl-xL levels. In summary, the results of the present study suggest that LIN may improve the therapeutic index of anthracyclines in the management of breast cancer, especially in MDR tumors